Light Without Trajectory: A Mathematical and Empirical No-Go Theorem

This work demonstrates that the concept of light propagating through space does not correspond to any definable or measurable physical quantity. Using the mathematical structure of relativistic spacetime, the operator content of quantum electrodynamics, and high-precision experimental evidence, a strict no-go theorem is established: electromagnetic radiation admits no internal temporal evolution and therefore no physically meaningful trajectory between emission and absorption. Because lightlike intervals possess zero proper time, no internal ordering, dynamical process, or experienced history can exist for light. Quantum electrodynamics independently confirms this result through the absence of a Lorentz-covariant photon position operator. Modern timing experiments, including optical clock time-transfer, Lorentz-invariance tests, and pulsar timing arrays, constrain any propagation-associated temporal structure to below 10^-18 seconds, with no detectable signal across more than twenty orders of magnitude in experimental sensitivity. Taken together, these results show that electromagnetic phenomena consist exclusively of emission events, absorption events, and correlations between them. No experiment reveals an intermediate physical process attributable to photon motion. A unified structural interpretation is proposed in which light is understood not as a traveling object, but as a null boundary of spacetime realizability. In this view, illumination, refraction, gravitational lensing, and black-hole shadows arise from the structure of admissible spacetime connectivity itself, without introducing new fields, equations, or modifications of established physical theory.